The Nationals had a four-game winning streak snapped, losing the finale of the three-game series after giving up just three runs during the first two contests.
Washington reliever Tyler Clippard came on in the seventh inning with two on and two away. He promptly issued a walk to load the bases but struck out Nick Hundley to end the threat and preserve the Nationals' 1-0 lead.
Clippard (1-2) stayed in the game for the eighth but gave up a one-out single to Orlando Hudson and a bunt base hit to Cameron Maybin. That brought up Kotsay, who hit a 2-1 pitch to right and drove in both runners.
The win went to Andrew Cashner (1-1), who worked a perfect eighth inning. Huston Street allowed a two-out single in the ninth before collecting his second save.
San Diego had lost its previous two games. The lone run for the Nationals came on a seventh-inning homer by Jayson Werth.